In Washington State:
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Do you need to hire an electrical contractor to repair your household appliance?

If your household appliance is cord-and-plug connected, then:

Neither an electrical contractor's license or an electrician is needed to install or replace (plug in) the appliance. The electrical law does not regulate repair work done in the appliance repair shop environment. Electrical contractor licensing and a certified electrician is required for repair work done on the owner's premises.

If your household appliance is hard-wired, then:

An electrical contractor utilizing properly certified electricians must be used to install, repair or replace the appliance.
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--from http://www.lni.wa.gov/TradesLicensing/Electrical/BasicElectInstall/Appliances/Default.asp